Publications related to Normal approximation of the solution to the stochastic heat equation with Levy noise

Gaussian and sparse processes are limits of generalized Poisson processes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

The n-term Approximation of Periodic Generalized Levy Processes

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

SPRINGER/PLENUM PUBLISHERS2020

The Almost-Sure Asymptotic Behavior Of The Solution To The Stochastic Heat Equation With Levy Noise

Carsten Hao Ye Chong

We examine the almost-sure asymptotics of the solution to the stochastic heat equation driven by a Levy space-time white noise. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high peaks over short tim ...

INST MATHEMATICAL STATISTICS2020

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k >= 1

Robert Dalang, Fei Pu

We establish a sharp estimate on the negative moments of the smallest eigenvalue of the Malliavin matrix gamma z of Z := (u(s, y), u(t , x) - u(s, y)), where u is the solution to a system of d non-linear stochastic heat equations in spatial dimension k >= ...

UNIV WASHINGTON, DEPT MATHEMATICS2020

Exceptional graphs for the random walk

Juhan Aru

If W is the simple random walk on the square lattice Z(2), then W induces a random walk W-G on any spanning subgraph G subset of Z(2) of the lattice as follows: viewing W as a uniformly random infinite word on the alphabet {x, -x, y, -y}, the walk W-G star ...

INST MATHEMATICAL STATISTICS2020

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Michaël Unser, Julien René Pierre Fageot

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

SPRINGER/PLENUM PUBLISHERS2019

A central limit theorem for functions of stationary max-stable random fields on R-d

Erwan Fabrice Koch, Clément Dombry

Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural disasters, meaning t ...

ELSEVIER2019

Path properties of the solution to the stochastic heat equation with Levy noise

Robert Dalang, Carsten Hao Ye Chong, Thomas Marie Jean-Baptiste Humeau

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

SPRINGER2019

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

Michaël Unser, Julien René Pierre Fageot, Anaïs Laure Marie-Thérèse Badoual

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational and statistical ...

2018

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Normal approximation of the solution to the stochastic heat equation with Levy noise

Gaussian and sparse processes are limits of generalized Poisson processes

The n-term Approximation of Periodic Generalized Levy Processes

The Almost-Sure Asymptotic Behavior Of The Solution To The Stochastic Heat Equation With Levy Noise

Increasing risk: Dynamic mean-preserving spreads

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k >= 1

Exceptional graphs for the random walk

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

A central limit theorem for functions of stationary max-stable random fields on R-d

Path properties of the solution to the stochastic heat equation with Levy noise

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

Graph Chatbot

Chat with Graph Search

The n-term Approximation of Periodic Generalized Levy Processes

The Almost-Sure Asymptotic Behavior Of The Solution To The Stochastic Heat Equation With Levy Noise

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

Path properties of the solution to the stochastic heat equation with Levy noise

A central limit theorem for functions of stationary max-stable random fields on R-d

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Exceptional graphs for the random walk

Gaussian and sparse processes are limits of generalized Poisson processes

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k >= 1

Increasing risk: Dynamic mean-preserving spreads